I'm looking for non-destructive way to structurally attach a standard servo with LEGO bricks. I'm interested in answers for either Large, Medium or Small size servos.

I'm using LEGO Mindstorm/Technic bricks to prototype all kind of robotic projects and I often use non-LEGO parts for the electronics (e.g. Arduino, Servos, LEDs, ...). I'm always trying to find better ways to integrate those non-LEGO parts without damaging the LEGO bricks.

I'm aware that there are some commercial adaptors available on the market but I'm interested in creative homemade solutions (low-cost to no-cost).

For example: here is one way to attach a medium size servo to a LEGO Technic beam:

To add to this answer, I would also suggest looking at The Free Universal Construction Set. While they don't provide anything for integrating legos and servos specifically, there's a lot of examples of how to integrate Legos with non Legos components (some of which might make integrating a servo easier.)
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kaliatechNov 6 '12 at 19:06

It's cheap and found in many general goods store. The servo itself can be taped and supported on all four sides and/or the bottom to many types of lego brick surfaces.

You can also use double-side tape to mount a lego surface to a servo control horn. That provides nearly infinite mounting flexibility. However, the control horn attachment will not be very rigid or support a lot of weight without an additional structures to support whatever is actually moving.

When finished, you can just peel the tape off. (...which is sometimes easier said than done.)